Long-time behavior of 3–dimensional Ricci flow, D : Proof of the main results

Bamler, Richard

doi:10.2140/gt.2018.22.949

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Long-time behavior of $3$–dimensional Ricci flow, D: Proof of the main results

Richard H Bamler

Geometry & Topology 22 (2018) 949–1068

DOI: 10.2140/gt.2018.22.949

Abstract

This is the fourth and last part of a series of papers on the long-time behavior of $3$ –dimensional Ricci flows with surgery. In this paper, we prove our main two results. The first result states that if the surgeries are performed correctly, then the flow becomes nonsingular eventually and the curvature is bounded by $C t^{- 1}$ . The second result provides a qualitative description of the geometry as $t \to \infty$ .

Keywords

Ricci flow, Ricci flow with surgery, finitely many surgeries, asymptotics of Ricci flow, collapsing theory of $3$–manifolds, topology of $3$–manifolds, geometrization conjecture

Mathematical Subject Classification 2010

Primary: 53C44

Secondary: 49Q05, 53C23, 57M15, 57M20

References

Publication

Received: 16 December 2014

Revised: 22 December 2016

Accepted: 21 January 2017

Published: 16 January 2018

Proposed: Tobias H. Colding

Seconded: Bruce Kleiner, Gang Tian

Authors

Richard H Bamler
Department of Mathematics University of California Berkeley, CA United States
https://math.berkeley.edu/~rbamler/

Volume 22, issue 2 (2018)